The Geometer's Sketchpad
Modeling a Ferris Wheel

Using Translations and Animation

Physical devices can be modeled using dynamic geometry. A vital tool for
moving objects around in the model are the isometries, or distance-preserving
transformations. This model of a Ferris wheel provides a good example.

This Ferris wheel has just one seat. Let's add more seats. We will
do this by constructing 3 more points on the circle to which we will attach the
seats. These points, along with C, will make four points, equally spaced 90
degrees apart around the circle.

Construct these points by constructing the line AC and then the line through
A perpendicular to line AC. The points of intersection of these lines with the
circle are the four equally spaced points.

Run the animation again to see how the four points move in unison. Hide the
two lines for esthetic reasons.

Now in turn mark the vector from the same vertex of the blob as before to
each of these three new points. Each time you mark a vector, translate the
blob by this vector.